How to prove that this is a parallelogram n how to find its area?
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Given: ABCD is a quadrilateral and BD is one of its diagonals.
To Prove: ABCD is a parallelogram and to determine its area.
Proof: ∠ABD = ∠BDC (= 90°) | Given But these angles form a pair of equal alternate
interior angles for lines AB, DC and a transversal BD AB || DC
Also, AD = DC (= 3 cm) | Given
Hence, quadrilateral ABCD is a parallelogram. A quadrilateral is a parallelogram if its one pair of opposite sides are parallel and equal Now,
ar(||gm ABCD) = Base x corresponding altitude
= 3x4 = 12 cm2
The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.
To Prove: ABCD is a parallelogram and to determine its area.
Proof: ∠ABD = ∠BDC (= 90°) | Given But these angles form a pair of equal alternate
interior angles for lines AB, DC and a transversal BD AB || DC
Also, AD = DC (= 3 cm) | Given
Hence, quadrilateral ABCD is a parallelogram. A quadrilateral is a parallelogram if its one pair of opposite sides are parallel and equal Now,
ar(||gm ABCD) = Base x corresponding altitude
= 3x4 = 12 cm2
The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.
jesnaharshad:
It is supposed to be AB=DC=3cm?
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